论文标题
边界稳定和观察多维不稳定热方程
Boundary stabilization and observation of a multi-dimensional unstable heat equation
论文作者
论文摘要
在本文中，我们考虑了多维不稳定热方程的边界稳定和观察。由于我们考虑了一般域中的热方程，因此很难适用于所考虑的问题，通常的偏微分方程后启动方法很难应用。通过结合有限维光谱截断方法和动力补偿方法来处理热方程的不稳定动力学。通过引入其他有限维的执行器/传感器动力学，无界的稳定/观察变成有限的稳定/观察。结果，控制器/观察者的设计变得更加容易。全州反馈稳定器和州观察员都设计了。获得了闭环的指数稳定性和观察者的良好性。
In this paper, we consider the boundary stabilization and observation of the multidimensional unstable heat equation. Since we consider the heat equation in a general domain, the usual partial differential equation back-stepping method is hard to apply to the considered problems. The unstable dynamics of the heat equation are treated by combining the finite-dimensional spectral truncation method and the dynamics compensation method. By introducing additional finite-dimensional actuator/sensor dynamics, the unbounded stabilization/observation turns to be a bounded one. As a result, the controller/observer design becomes more easier. Both the full state feedback stabilizer and the state observer are designed. The exponential stability of the closed-loop and the wellposedness of the observer are obtained.
